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Simulating An AR Process With A Specified Covariance
Syntax arcov(N, M, r)
See Also filter , snormal , fspec

Description
Returns M columns, each of which is a realization of a Gaussian AR process with an order that is one less than the row dimension of r, where N is an integer scalar specifying the number of points in each realization of the AR process, M is an integer scalar specifying the number of realizations, and r is a real or double-precision column vector such that for L = 1 to the row dimension of r, the expected value of x(i,j) * x(i + L - 1,j) is equal to r(L). The return value has N rows, M columns, and the same type as r.

If x is a Gaussian AR process of order m, there is a vector, a, such that
     x = a  w  + a  x   + ... + a  x
      n   0  n    1  n-1         m  n-m
where the {w(n)} are independent, normal, and have a mean of 0 and a variance of 1.

Example
     N = 200
     M = 1
     r = {1., .9}
     y = arcov(N, M, r)
     gtitle("AR(1) Simulation")
     gplot(seq(N), y, "plus")

 returns the following plot: